Solve for $x$ and $y$ using elimination. ${-x+5y = 0}$ ${x-4y = 1}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x+5y = 0}\thinspace$ to find $x$ ${-x + 5}{(1)}{= 0}$ $-x+5 = 0$ $-x+5{-5} = 0{-5}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {x-4y = 1}\thinspace$ and get the same answer for $x$ : ${x - 4}{(1)}{= 1}$ ${x = 5}$